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# Shady Symmetry

## You may also like

### Rhombicubocts

### Prime Magic

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 11 to 14

Challenge Level

*Shady Symmetry printable sheet - problem
Shady Symmetry downloadable slides - images
Printable isometric grid template*

Charlie created a symmetrical pattern by shading in four squares on a 3 by 3 square grid:

Alison created a symmetrical pattern by shading in two triangles on a 3 by 3 isometric grid:

Choose whether you would like to work on square grids or isometric grids.

How many different symmetrical patterns can you make?

Here are some questions you might like to consider:

- How many different patterns can you make if you are only allowed to shade in one... two... three... four cells?
- How does the number of patterns with 6 cells shaded relate to the number with 3 cells shaded?
- Can you make patterns with exactly one... two... three... four lines of symmetry?
- Can you make patterns with rotational symmetry AND lines of symmetry?
- Can you make patterns with rotational symmetry but NO lines of symmetry?
- Can you make patterns using more than one colour?

Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?